Problem: Recently you have bought a snow walking robot and brought it home. Suppose your home is a cell (0, 0) on an infinite grid.

You also have the sequence of instructions of this robot. It is written as the string s consisting of characters 'L', 'R', 'U' and 'D'. If the robot is in the cell (x, y) right now, he can move to one of the adjacent cells (depending on the current instruction).

  * If the current instruction is 'L', then the robot can move to the left to (x - 1, y); 
  * if the current instruction is 'R', then the robot can move to the right to (x + 1, y); 
  * if the current instruction is 'U', then the robot can move to the top to (x, y + 1); 
  * if the current instruction is 'D', then the robot can move to the bottom to (x, y - 1). 



You've noticed the warning on the last page of the manual: if the robot visits some cell (except (0, 0)) twice then it breaks.

So the sequence of instructions is valid if the robot starts in the cell (0, 0), performs the given instructions, visits no cell other than (0, 0) two or more times and ends the path in the cell (0, 0). Also cell (0, 0) should be visited at most two times: at the beginning and at the end (if the path is empty then it is visited only once). For example, the following sequences of instructions are considered valid: "UD", "RL", "UUURULLDDDDLDDRRUU", and the following are considered invalid: "U" (the endpoint is not (0, 0)) and "UUDD" (the cell (0, 1) is visited twice).

The initial sequence of instructions, however, might be not valid. You don't want your robot to break so you decided to reprogram it in the following way: you will remove some (possibly, all or none) instructions from the initial sequence of instructions, then rearrange the remaining instructions as you wish and turn on your robot to move. 

Your task is to remove as few instructions from the initial sequence as possible and rearrange the remaining ones so that the sequence is valid. Report the valid sequence of the maximum length you can obtain.

Note that you can choose any order of remaining instructions (you don't need to minimize the number of swaps or any other similar metric).

You have to answer q independent test cases.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 2 ⋅ 10^4) — the number of test cases.

The next q lines contain test cases. The i-th test case is given as the string s consisting of at least 1 and no more than 10^5 characters 'L', 'R', 'U' and 'D' — the initial sequence of instructions.

It is guaranteed that the sum of |s| (where |s| is the length of s) does not exceed 10^5 over all test cases (∑ |s| ≤ 10^5).

Output

For each test case print the answer on it. In the first line print the maximum number of remaining instructions. In the second line print the valid sequence of remaining instructions t the robot has to perform. The moves are performed from left to right in the order of the printed sequence. If there are several answers, you can print any. If the answer is 0, you are allowed to print an empty line (but you can don't print it).

Example

Input


6
LRU
DURLDRUDRULRDURDDL
LRUDDLRUDRUL
LLLLRRRR
URDUR
LLL


Output


2
LR
14
RUURDDDDLLLUUR
12
ULDDDRRRUULL
2
LR
2
UD
0

Note

There are only two possible answers in the first test case: "LR" and "RL".

The picture corresponding to the second test case:

<image> Note that the direction of traverse does not matter 

Another correct answer to the third test case: "URDDLLLUURDR".

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

public class Robots{

    static BufferedReader input = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws IOException {

        String linea;
        linea = input.readLine();
        int casos = Integer.parseInt(linea);

        while(casos > 0){
            StringBuilder str = new StringBuilder(input.readLine());
            int U = 0,D = 0,R = 0,L = 0;
            for(int i = 0 ; i < str.length() ; i ++ ){
                char letra = str.charAt(i);
                if(letra ==  'U'){
                    U++;
                }

                else if(letra ==  'D'){
                    D++;
                }
                else if(letra ==  'R'){
                    R++;
                }
                if(letra ==  'L'){
                    L++;
                }
            }

            if(U > D){
                U = D;
            }

            else{
                D = U;
            }

            if(R > L){
                R = L;
            }

            else{
                L = R;
            }

            if(U == 0 && R > 1){
                R = 1;
                L = 1;
            }
            else if(R == 0 && U > 1){
                U = 1;
                D = 1;
            }
            
            int movimientos = U+D+R+L;
            System.out.println(movimientos);

            while(U > 0){
                System.out.print("U");
                U--;
            }
            while(L > 0){                
                System.out.print("L");
                L--;
            }
            while(D > 0){
                System.out.print("D");
                D--;
            }
            while(R > 0){
                System.out.print("R");
                R--;
            }
            System.out.print("\n");

            casos--;
        }

        
        
    }

}

interface Robot{

    public String[] movimientos(StringBuilder U , StringBuilder D , StringBuilder R, StringBuilder L);


}

 class caminante implements Robot{

    public String[] movimientos(StringBuilder U , StringBuilder D , StringBuilder R, StringBuilder L){
            int cantidad_U = U.length();
            int cantidad_D = D.length();
            int cantidad_R = R.length();
            int cantidad_L = L.length();

            int Movimientos_totales = 0;

    
            if(cantidad_U > cantidad_D){
                cantidad_U = cantidad_D;
            }
    
            else{
                cantidad_D = cantidad_U;
            }
    
            if(cantidad_R > cantidad_L){
                cantidad_R = cantidad_L;
            }
    
            else{
                cantidad_L = cantidad_R;
            }

            

            if(cantidad_U == 0 && cantidad_R > 1){
                cantidad_R = 1;
                cantidad_L = 1;
            }
            else if(cantidad_R == 0 && cantidad_U > 1){
                cantidad_U = 1;
                cantidad_U = 1;
            }

            Movimientos_totales = cantidad_U + cantidad_D + cantidad_L + cantidad_R;

            String Us = U.subSequence(0, cantidad_U).toString();
            String Ds = U.subSequence(0, cantidad_D).toString();
            String Rs = U.subSequence(0, cantidad_R).toString();
            String Ls = U.subSequence(0, cantidad_L).toString();
        
            
            String[] retorno = {Integer.toString(Movimientos_totales),Us,Ds,Rs,Ls};
            return  retorno;
    }

}

class saltador implements Robot{
    public String[] movimientos(StringBuilder U , StringBuilder D , StringBuilder R, StringBuilder L){
        //se calcula todos largos para comparar
        int cantidad_U = 0;
        int cantidad_D = 0;
        int cantidad_R = 0;
        int cantidad_L = 0;

        int Movimientos_totales = U.length() + D.length() + R.length() + L.length();

        for(int i = 0 ; i <= U.length() ; i++){
            if(U.charAt(i) ==  '1'){
                cantidad_U++;
            }

            else{
                cantidad_U += 2;
            }

        }

        for(int i = 0 ; i <= D.length() ; i++){
            if(U.charAt(i) ==  '1'){
                cantidad_D++;
            }

            else{
                cantidad_D += 2;
            }

        }
        for(int i = 0 ; i <= R.length() ; i++){
            if(U.charAt(i) ==  '1'){
                cantidad_R++;
            }

            else{
                cantidad_R += 2;
            }

        }
        for(int i = 0 ; i <= L.length() ; i++){
            if(U.charAt(i) ==  '1'){
                cantidad_L++;
            }

            else{
                cantidad_L += 2;
            }

        }
        

        

        //para igualar alturas
        int resta = cantidad_U - cantidad_D;
        while(resta != 0){
            //caso que sea mayor que 2
            if(resta >= 2 || resta <= -2){
                //caso de que u sea mayor que d
                if(cantidad_U > cantidad_D){
                    if(U.indexOf("2")!= -1){
                        int index = U.indexOf("2");
                        if (index == 0){
                             U = U.delete(0, 1);
                             Movimientos_totales --;
                        }
                        else if (index == U.length()){
                            U = U.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            U = U.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int n = 2;
                        while(n > 0){
                            int index = U.indexOf("1");
                            if (index == 0){
                                U = U.delete(0, 1);
                                Movimientos_totales --;
                            }
                            else if (index == U.length()){
                                U = U.delete(index, index);
                                Movimientos_totales --;
                            }
                            else{
                                U = U.delete(index-1,index+1);
                                Movimientos_totales --;
                            }
                        }
                    }
                }
                //caso que D sea mayor que U
                else{
                    if(D.indexOf("2")!= -1){
                        int index = D.indexOf("2");
                        if (index == 0){
                            D = D.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == D.length()){
                            D = D.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            D = D.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int n = 2;
                        while(n > 0){
                            int index = D.indexOf("1");
                            if (index == 0){
                                D = D.delete(0, 1);
                                Movimientos_totales --;
                            }
                            else if (index == D.length()){
                                D = D.delete(index, index);
                                Movimientos_totales --;
                            }
                            else{
                                D = D.delete(index-1,index+1);
                                Movimientos_totales --;
                            }
                        }
                    }
                }

            }
            // caso que tengan uno de diferencia
            else{
                //caso de que u sea mayor que D
                if(cantidad_U > cantidad_D){
                    if(U.indexOf("1")!= -1){
                        int index = U.indexOf("1");
                        if (index == 0){
                            U = U.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == U.length()){
                            U = U.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            U = U.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int index = U.indexOf("2");
                        if (index == 0){
                            U = U.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == U.length()){
                            U = U.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            U = U.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                        index = D.indexOf("1");
                        if (index == 0){
                            D = D.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == D.length()){
                            D = D.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            D = D.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                    }
                }
                //Caso de que D sea mayor que U
                else{
                    if(D.indexOf("1")!= -1){
                        int index = D.indexOf("1");
                        if (index == 0){
                            D = D.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == D.length()){
                            D = D.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            D = D.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int index = D.indexOf("2");
                        if (index == 0){
                            D = D.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == D.length()){
                            D = D.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            D = D.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                        index = U.indexOf("1");
                        if (index == 0){
                            U = U.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == U.length()){
                            U = U.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            U = U.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                    }
                    
                }
            }
            // se recalcula la altura
            cantidad_U = 0 ;
            cantidad_D = 0;
            for(int i = 0 ; i <= U.length() ; i++){
                if(U.charAt(i) ==  '1'){
                    cantidad_U++;
                }
    
                else{
                    cantidad_U += 2;
                }
    
            }
    
            for(int i = 0 ; i <= D.length() ; i++){
                if(U.charAt(i) ==  '1'){
                    cantidad_D++;
                }
    
                else{
                    cantidad_D += 2;
                }
    
            }
            resta = cantidad_U - cantidad_D;

        }
        //aqui termina de igualar alturas
        

        //para igualar movimientos laterales(se hace igual que en altura)
        
        resta = cantidad_R - cantidad_L;
        while(resta != 0){
            //caso que sea mayor que 2
            if(resta >= 2 || resta <= -2){
                //caso de que R sea mayor que L
                if(cantidad_R > cantidad_L){
                    if(R.indexOf("2")!= -1){
                        int index = R.indexOf("2");
                        if (index == 0){
                             R = R.delete(0, 1);
                             Movimientos_totales --;
                        }
                        else if (index == R.length()){
                            R = R.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            R = R.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int n = 2;
                        while(n > 0){
                            int index = R.indexOf("1");
                            if (index == 0){
                                R = R.delete(0, 1);
                                Movimientos_totales --;
                            }
                            else if (index == R.length()){
                                R = R.delete(index, index);
                                Movimientos_totales --;
                            }
                            else{
                                R = R.delete(index-1,index+1);
                                Movimientos_totales --;
                            }
                        }
                    }
                }
                //caso que L sea mayor que R
                else{
                    if(L.indexOf("2")!= -1){
                        int index = L.indexOf("2");
                        if (index == 0){
                            L = L.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == L.length()){
                            L = L.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            L = L.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int n = 2;
                        while(n > 0){
                            int index = L.indexOf("1");
                            if (index == 0){
                                L = L.delete(0, 1);
                                Movimientos_totales --;
                            }
                            else if (index == L.length()){
                                L = L.delete(index, index);
                                Movimientos_totales --;
                            }
                            else{
                                L = L.delete(index-1,index+1);
                                Movimientos_totales --;
                            }
                        }
                    }
                }
            }
            // caso que tengan uno de diferencia
            else{
                //caso de que R sea mayor que L
                if(cantidad_R > cantidad_L){
                    if(R.indexOf("1")!= -1){
                        int index = R.indexOf("1");
                        if (index == 0){
                            R = R.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == R.length()){
                            R = R.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            R = R.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int index = R.indexOf("2");
                        if (index == 0){
                            R = R.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == R.length()){
                            R = R.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            R = R.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                        index = L.indexOf("1");
                        if (index == 0){
                            L = L.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == L.length()){
                            L = L.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            L = L.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                    }
                }
                //Caso de que L sea mayor que U
                else{
                    if(L.indexOf("1")!= -1){
                        int index = L.indexOf("1");
                        if (index == 0){
                            L = L.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == L.length()){
                            L = L.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            L = L.delete(index-1,index+1);
                            Movimientos_totales --;
                        }
                    }
                    else{
                        int index = L.indexOf("2");
                        if (index == 0){
                            L = L.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == L.length()){
                            L = L.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            L = L.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                        index = R.indexOf("1");
                        if (index == 0){
                            R = R.delete(0, 1);
                            Movimientos_totales --;
                        }
                        else if (index == R.length()){
                            R = R.delete(index, index);
                            Movimientos_totales --;
                        }
                        else{
                            R = R.delete(index-1,index+1);
                            Movimientos_totales --;
                        }

                    }
                    
                }
            }
            // se recalcula el movimiento lateral
            cantidad_R = 0 ;
            cantidad_L = 0;
            for(int i = 0 ; i <= R.length() ; i++){
                if(R.charAt(i) ==  '1'){
                    cantidad_R++;
                }
    
                else{
                    cantidad_R += 2;
                }
    
            }
    
            for(int i = 0 ; i <= L.length() ; i++){
                if(L.charAt(i) ==  '1'){
                    cantidad_L++;
                }
    
                else{
                    cantidad_L += 2;
                }
    
            }
            resta = cantidad_R - cantidad_L;


        }

        StringBuilder Us = new StringBuilder();
        StringBuilder Ds = new StringBuilder();
        StringBuilder Rs = new StringBuilder();
        StringBuilder Ls = new StringBuilder();

        if(cantidad_U == 0 && cantidad_R > 1){
            if(R.indexOf("1") != -1 && L.indexOf("1") !=  -1){
                R.append("R");
                R.append("1");
                L.append("L");
                L.append("1");
            }
        }

        else if(cantidad_R == 0 && cantidad_U > 1){
            if(U.indexOf("1") != -1 && D.indexOf("1") != -1){
                U.append("U");
                U.append("1");
                D.append("D");
                D.append("1");
            }

        }

        else{
            
            for(int i = 0;i<U.length(); i++ ){
                Us.append("U");
                Us.append(U.charAt(i));
    
            }
            for(int i = 0;i<D.length(); i++ ){
                Us.append("D");
                Us.append(D.charAt(i));
    
            }
            for(int i = 0;i<R.length(); i++ ){
                Us.append("R");
                Us.append(R.charAt(i));
    
            }
            for(int i = 0;i<L.length(); i++ ){
                Us.append(L);
                Us.append(L.charAt(i));
    
            }

        }


        //me falta ver el caso que tenga una subida nada mas
        

                    
        String[] retorno = {Integer.toString(Movimientos_totales),Us.toString(),Ds.toString(),Rs.toString(),Ls.toString()};
         return  retorno;
    
    }   
    
}


class Handler{

    public String[] input(StringBuilder Comandos){
        

        boolean Saltador = true;
        //0 < no esta presente en "12", por lo tanto es de tipo caminante
        if("12".indexOf(Comandos.charAt(2)) == -1){
            Saltador = false;
        }

        //caso que sea de tipo saltador
        if(Saltador){

            StringBuilder Us = new StringBuilder();
            StringBuilder Ds = new StringBuilder();
            StringBuilder Rs = new StringBuilder();
            StringBuilder Ls = new StringBuilder();

            //necesarios para agregar una letra
            char l = 'n';
            boolean EsNumero = false;

            for(int i = 0 ; i < Comandos.length() ; i ++ ){
                char letra = Comandos.charAt(i);
                if(EsNumero){
                    if(l ==  'U'){
                        Us.append(letra);
                    }
        
                    else if(l ==  'D'){
                        Ds.append(letra);
                    }
                    else if(l ==  'R'){
                        Rs.append(letra);
                    }
                    else if(l ==  'L'){
                        Ls.append(letra);
                    }
                    EsNumero = false;
                }

                else{
                    l = letra;
                    EsNumero = true;
                }

                
            }




            String[] cosa = {"error"} ;
            return cosa;
        }
        // caso que sea caminante normal
        else{

            StringBuilder Us = new StringBuilder();
            StringBuilder Ds = new StringBuilder();
            StringBuilder Rs = new StringBuilder();
            StringBuilder Ls = new StringBuilder();
            
            for(int i = 0 ; i < Comandos.length() ; i ++ ){
                char letra = Comandos.charAt(i);
                if(letra ==  'U'){
                    Us.append("U");
                }
    
                else if(letra ==  'D'){
                    Ds.append("D");
                }
                else if(letra ==  'R'){
                    Rs.append("R");
                }
                else if(letra ==  'L'){
                    Ls.append("L");
                }
            }

            caminante RobotCaminante = new caminante();
            
            
            
            return RobotCaminante.movimientos(Us, Ds, Rs, Ls);
            


        }

          
    }


}